High power microelectronic packages dissipate large densities of thermal energy. An array of thermal vias may be used to provide a thermal channel through a substrate to direct thermal energy away from an operating electronic device. Via-bar structures, similar to thermal vias yet having a greater heat-conducting cross-sectional area, have been increasingly used to reduce thermal resistances in the thermal channel as compared to thermal vias. However, conventional via-bar structures may be associated with package stress and, therefore, reduced device reliability.